Uniqueness and stability of nonnegative solutions for semipositone problems in a ball
HTML articles powered by AMS MathViewer
- by Ismael Ali, Alfonso Castro and R. Shivaji PDF
- Proc. Amer. Math. Soc. 117 (1993), 775-782 Request permission
Abstract:
We study the uniqueness and stability of nonnegative solutions for classes of nonlinear elliptic Dirichlet problems on a ball, when the nonlinearity is monotone, negative at the origin, and either concave or convex.References
- K. J. Brown, Alfonso Castro, and R. Shivaji, Nonexistence of radially symmetric nonnegative solutions for a class of semi-positone problems, Differential Integral Equations 2 (1989), no. 4, 541–545. MR 996760
- K. J. Brown and R. Shivaji, Instability of nonnegative solutions for a class of semipositone problems, Proc. Amer. Math. Soc. 112 (1991), no. 1, 121–124. MR 1043405, DOI 10.1090/S0002-9939-1991-1043405-5 A. Castro, J. B. Garner, and R. Shivaji, Existence results for a class of sublinear semipositone problems, Result. Math. (to appear).
- Alfonso Castro and R. Shivaji, Nonnegative solutions for a class of nonpositone problems, Proc. Roy. Soc. Edinburgh Sect. A 108 (1988), no. 3-4, 291–302. MR 943804, DOI 10.1017/S0308210500014670
- Alfonso Castro and R. Shivaji, Nonnegative solutions for a class of radially symmetric nonpositone problems, Proc. Amer. Math. Soc. 106 (1989), no. 3, 735–740. MR 949875, DOI 10.1090/S0002-9939-1989-0949875-3
- Alfonso Castro and R. Shivaji, Nonnegative solutions to a semilinear Dirichlet problem in a ball are positive and radially symmetric, Comm. Partial Differential Equations 14 (1989), no. 8-9, 1091–1100. MR 1017065, DOI 10.1080/03605308908820645
- B. Gidas, Wei Ming Ni, and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), no. 3, 209–243. MR 544879
- D. H. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J. 21 (1971/72), 979–1000. MR 299921, DOI 10.1512/iumj.1972.21.21079
- Joel Smoller and Arthur Wasserman, Existence of positive solutions for semilinear elliptic equations in general domains, Arch. Rational Mech. Anal. 98 (1987), no. 3, 229–249. MR 867725, DOI 10.1007/BF00251173 G. Sweers, Semilinear elliptic eigenvalue problems, Doctoral Thesis, Univ. of Leiden, Netherlands, 1988. S. Unsurangsie, Existence of a solution for a wave equation and an elliptic Dirichlet problem, Doctoral Thesis, Univ. of North Texas, 1988.
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 775-782
- MSC: Primary 35J65; Secondary 35B32, 35B35, 35P30
- DOI: https://doi.org/10.1090/S0002-9939-1993-1116249-5
- MathSciNet review: 1116249